ECAT Mathematics MCQ's Test For Full Book With Answers

ECAT Mathematics MCQ's Test For Full Book

Sr. # Questions Answers Choice
1 The points (-1,3), (3,0) are the vertices of: Right-angled triangle Isosceles triangle Equilateral triangle square
2 The quadrilateral with the vertices (-3,-2), (2,-1), (3,4) and (-2,3) is a: Square Rectangle rhombus parallelogram
3 The points (5,2),(-2,3),(-3,-4) and (4,-5) are the vertices of: rhombus Parallelogram rectangle square
4 The points (3,1), (-2,-3) and (2,2) are the vertices of : Equilateral triangle Isosceles triangle right -angled triangle rhombus
5 The cartesian system of coordinates was introduced by: Eulaer Euclid Descrates Maclream
6 The solution of differential equation: dy/dx+y/x = x<sup>2 </sup>is : 4xy = x<sup>4</sup>+ c 4x = x<sup>4</sup>= c 4 y = x<sup>4</sup>+ c 4x=4x<sup>3</sup> + c
7 An equation in which at least one term contains dy/dx, d2 y /dx2etc, is called. Differential equation Initial condition General solution Singular equation
8 The general solution of the differential equation x dy / dx = 1 + y is: 2 1 3 None
9 The area enclosed between the graph y = x2 -4x and the x- axis is: 20/3 41/3 32/3 25/3
10 The area under the curve y = 1/x2 between x = 1 and x =4 is: -25 0.75 -0.35 -10
11 The area between the x-axis the curve y =4x-x2 is : 32/2 15 18 21
12 The area between the x-axis and the curve y = x2 + 1 from x = 1 to 2 is: 15/6 15/4 10/4 10/3
13 ∫x/Sin2 x dx is equal to: x cot x + ln|sin⁡x | -x cot x - ln|sin⁡x | x cot x - ln|sin⁡x | x. tan x- ln|sec⁡x |
14 ∫x sin xdx is equal to: sin x/x + cos x sin x - cos x/x x cos x + sin x - x cos x + sin x
15 ∫ x cos dx is equal to : x cos x + sin x cos x + x sin x x cos x + x sin x x sin x + cos x
16 ∫sin(ax+b) dx is equal to: 1/2a cos (ax + b) -1/a cos (ax +b) 1/a cos (ax +b) 1/a ln (ax + b)
17 ∫Sec2 (ax + b) dx is equal to: tan<sup>2</sup> (ax + b) 1/a tan<sup>2</sup> (ax + b) 1/atan (ax +b) tan (ax + b)
18 The integral of 3x5dx is: 15 x<sup>4</sup> x<sup>6 </sup>/2 1/6x<sup>5</sup> x<sup>5 </sup>/ln3
19 ∫f(x) is known as: Definite itegral Indefinite integral Fixed integral Multiple integral
20 An integral of 1/x dx is: 1/x<sup>2</sup> 1/-x<sup>2</sup> 1/lnx lnx
21 If y = 3 x + 2cos x, then dy/dx = 3-2 sin x 3-t sin x 3x<sup>2</sup> - 2sin x 3(1-4 sin x)
22 d/dx (cos x sin x) = cos<sup>2</sup> x - sin<sup>2</sup> x 2cos<sup>2 </sup>x + sin<sup>2</sup> x 2cos<sup>2</sup> x - sin<sup>2</sup> x 1 - sin<sup>2 </sup>x
23 d/dx (cosec x) -sec x tan x sin x cos x -csc x cot x 2sin x cos x
24 d / dx (cot x) = Sec x tan x -csc<sup>2</sup> x Sec<sup>2</sup> x 1/cot<sup>2</sup> x
25 d/dx (cos x2) = -2x cos x -2x sin x<sup>2</sup> -2x tan x -2x sec<sup>2</sup> x
26 d/dx [tan2 x] 2tan x sec<sup>2</sup> x 2tan x sec x 2 cot x tan x 2sec<sup>2</sup> x cos<sup>2</sup> x
27 Differentiation of sin x w.r.t. cot x is: -sin<sup>2</sup> x sec x -cos x sin<sup>2</sup> x -cos<sup>2</sup> x tan x -sin<sup>2</sup> x
28 If∱(x) = 1/x-2 then∱1(0) equals: -1/4 -3/2 -1/2 1/5
29 If∱(x) = c then∱1 (x0 equals: 1 0 cx c
30 If ∱(x) = x2/3then∱1(x) at x = 8 equals: 8 1/8 1/3 2/3
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